1. Field
This application relates generally to signal processing and more specifically, but not exclusively, to wireless telecommunication, signal acquisition and reconstruction.
2. Introduction
Signal acquisition and reconstruction is at the heart of signal processing, and sampling theorems provide the bridge between continuous time phenomena and discrete-time representations of such phenomena. A well-known sampling theorem is often attributed to Shannon, and gives a sufficient condition, namely bandlimitedness, for an exact sampling and interpolation formula. The minimal sampling rate, at twice the bandwidth of the analog signal, is typically referred to as the Nyquist rate.
The Shannon case is a particular example, where any signal from the subspace of bandlimited signals denoted by BL, can be acquired through sampling and perfectly interpolated from the samples. Using the sinc kernel, or ideal lowpass filter, non-bandlimited signals will be projected onto the subspace BL.
International Patent Application WO 02/078197, which is hereby incorporated by reference, develops sampling schemes for a larger class of non-bandlimited signals, such as streams of Diracs, non-uniform splines and piecewise polynomials. A common feature of these signals is that they have a parametric representation with a finite number of degrees of freedom (or a number which is finite in each period), and can be perfectly reconstructed from a finite set of samples.